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CBSE Class 12 · 2011 · DeterminantsLong Answer

Using the properties of determinants, solve the following for

x

:

a + x a - x a - x a - x a + x a - x a - x a - x a + x = 0.

Answer: $x = 0$ or $x = 3 a$ \,

Solution

Apply

C_{1} \to C_{1} + C_{2} + C_{3}

; every entry of column

1

becomes

3 a - x

. Take it common.

(3 a - x) 111 a - x a + x a - x a - x a - x a + x = 0.

Now

R_{2} \to R_{2} - R_{1}

,

R_{3} \to R_{3} - R_{1}

and expand:

(3 a - x) 100 a - x 2 x 0 a - x 0 2 x = (3 a - x) (2 x)^{2} = 0.

Hence

x = 0

(double) or

x = 3 a

.

x = 0 or x = 3 a

CBSE Class 12 Board · 2011 · Subjective

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